"""
https://leetcode-cn.com/problems/number-of-islands
https://leetcode-cn.com/problems/number-of-islands/solution/dfs-bfs-bing-cha-ji-python-dai-ma-java-dai-ma-by-l/
https://www.liwei.party/2019/01/18/algorithms-and-data-structures/union-find-set/
https://www.jb51.net/article/136687.htm

给定一个由 '1'（陆地）和 '0'（水）组成的的二维网格，计算岛屿的数量。
一个岛被水包围，并且它是通过水平方向或垂直方向上相邻的陆地连接而成的。
你可以假设网格的四个边均被水包围。

示例 1:
输入:
11110
11010
11000
00000

输出: 1

示例 2:
输入:
11000
11000
00100
00011

输出: 3

"""
from typing import List
from collections import deque


class Solution:

    def __init__(self):
        """
                 x-1, y
        x, y-1    x, y     x, y+1
                x+1, y

        方向数组，它表示了相对于当前位置的 4 个方向的横、纵坐标的偏移量，这是一个常见的技巧
        """
        self.directions = [(-1, 0), (0, 1), (1, 0), (0, -1)]

    def numIslands(self, grid: List[List[str]]) -> int:
        """
        提示：
        法一：深度优先搜索

        """
        m = len(grid)
        # 特判
        if m == 0:
            return 0
        n = len(grid[0])
        # marked 尺寸与 grid 一样，主要是用来标记哪一块已经处理过，处理过且是陆地的格子被标记为 True。
        marked = [[False for _ in range(n)] for _ in range(m)]
        count = 0
        # 从第 1 行、第 1 格开始，对每一格尝试进行一次 DFS 操作
        for i in range(m):
            for j in range(n):
                # 只要是陆地，且没有被访问过的，就可以使用 DFS 发现与之相连的陆地，并进行标记
                if not marked[i][j] and grid[i][j] == '1':
                    # count 可以理解为连通分量，你可以在深度优先遍历完成以后，再计数，
                    # 即这行代码放在【位置 1】也是可以的
                    count += 1
                    self.__dfs(grid, i, j, m, n, marked)
                    # 【位置 1】
        return count

    def __dfs(self, grid, i, j, m, n, marked):
        marked[i][j] = True
        for direction in self.directions:
            new_i = i + direction[0]
            new_j = j + direction[1]
            if 0 <= new_i < m and 0 <= new_j < n and not marked[new_i][new_j] and grid[new_i][new_j] == '1':
                self.__dfs(grid, new_i, new_j, m, n, marked)

    def numIslands2(self, grid: List[List[str]]) -> int:
        """
        提示：
        法二：广度优先搜索

        """
        m = len(grid)
        # 特判
        if m == 0:
            return 0
        n = len(grid[0])
        marked = [[False for _ in range(n)] for _ in range(m)]
        count = 0
        # 从第 1 行、第 1 格开始，对每一格尝试进行一次 BFS 操作
        for i in range(m):
            for j in range(n):
                # 只要是陆地，且没有被访问过的，就可以使用 BFS 发现与之相连的陆地，并进行标记
                if not marked[i][j] and grid[i][j] == '1':
                    # count 可以理解为连通分量，你可以在广度优先遍历完成以后，再计数，
                    # 即这行代码放在【位置 1】也是可以的
                    count += 1
                    queue = deque()
                    queue.append((i, j))
                    # 注意：这里要标记上已经访问过
                    marked[i][j] = True
                    while queue:
                        cur_x, cur_y = queue.popleft()
                        # 得到 4 个方向的坐标
                        for direction in self.directions:
                            new_i = cur_x + direction[0]
                            new_j = cur_y + direction[1]
                            # 如果不越界、没有被访问过、并且还要是陆地，我就继续放入队列，放入队列的同时，要记得标记已经访问过。
                            if 0 <= new_i < m and 0 <= new_j < n and \
                                    not marked[new_i][new_j] and grid[new_i][new_j] == '1':
                                queue.append((new_i, new_j))
                                # 【特别注意】在放入队列以后，要马上标记成已经访问过，语义也是十分清楚的：
                                # 反正只要进入了队列，你迟早都会遍历到它，而不是在出队列的时候再标记
                                # 【特别注意】如果是出队列的时候再标记，会造成很多重复的结点进入队列，
                                # 造成重复的操作，这句话如果你没有写对地方，代码会严重超时。
                                marked[new_i][new_j] = True
                    # 【位置 1】
        return count

    def numIslands3(self, grid: List[List[str]]) -> int:
        """
        提示：
        法三：并查集

        """
        class UnionFind:
            """
            定义简单的并查集
            这个并查集没有任何的优化，是最简单的版本。
            优化的版本可以看 leetcode 547 朋友圈 里写的并查集：
            """

            def __init__(self, n):
                self.count = n
                self.parent = [i for i in range(n)]

            def find(self, p):
                while p != self.parent[p]:
                    p = self.parent[p]
                return p

            def is_connected(self, p, q):
                return self.find(p) == self.find(q)

            def union(self, p, q):
                p_root = self.find(p)
                q_root = self.find(q)
                if p_root == q_root:
                    return
                self.parent[q_root] = p_root
                self.count -= 1

        row = len(grid)
        # 特判
        if row == 0:
            return 0
        col = len(grid[0])

        def get_index(x, y):
            # 把二维的地图从左往右，从上往下，编号为 0 ~ row * col，
            # 依次判断相邻的成员所属阵营（是否都是陆地）
            return x * col + y

        # 注意：我们不用像 DFS 和 BFS 一样，4 个方向都要尝试，只要看一看右边和下面就可以了
        directions = [(1, 0), (0, 1)]
        # 多开一个空间，把水域 "0" 都归到这个虚拟的老大上
        dummy_node = row * col

        # 多开的一个空间就是那个虚拟的空间
        uf = UnionFind(dummy_node + 1)
        for i in range(row):
            for j in range(col):
                # 如果是水域，都连到那个虚拟的空间去
                if grid[i][j] == '0':
                    uf.union(get_index(i, j), dummy_node)
                if grid[i][j] == '1':
                    # 向下、向右如果都是陆地，即 "1"，就要合并一下
                    for direction in directions:
                        new_x = i + direction[0]
                        new_y = j + direction[1]
                        if new_x < row and new_y < col and grid[new_x][new_y] == '1':
                            uf.union(get_index(i, j), get_index(new_x, new_y))
        # 不要忘记把那个虚拟结点减掉
        return uf.count - 1


if __name__ == '__main__':
    grid = [['1', '1', '0', '1', '0'],
            ['1', '0', '0', '1', '0'],
            ['0', '1', '0', '1', '1'],
            ['0', '1', '1', '0', '1']]
    grid2 = 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    solution = Solution()
    result = solution.numIslands(grid)
    print(result)
    result2 = solution.numIslands2(grid)
    print(result2)
    result3 = solution.numIslands3(grid)
    print(result3)

